小波纹矩形束管的阻抗
Impedance of a Rectangular Beam Tube with Small Corrugations
摘要：
我们考虑的阻抗的结构与矩形，周期性的波纹的两个相对侧的矩形束管。利用场匹配的方法，我们找到了这种结构中的模式。然后，我们将自己限制在小波纹的情况下，但是与周期相比，波纹的深度并不小。对于这样的结构，我们产生的波数$k$，群速度$v_g$，和损耗因子$κ$的最低（占主导地位）的模式，当与完整的数值解的结果相比，同意很好的解析近似解。我们发现：如果$w\sim a$，其中$w$是束管宽度，$a$是束管半高，则一种模式支配阻抗，具有$k\sim1/\sqrt{wδ}$（$δ$是波纹的深度）、$(1-v_g/c)\simδ$和$κ\sim1/(aw)$，其（当用$a$代替$w$时）与对于{ \it圆形}束管中的小波纹所发现的缩放相同。我们的结果不同意在一个重要的方式与最近的论文Mostacci { \it等人}。[A. Mostacci { \it等人}，Phys. Rev. ST-AB，{ \bf 5}，044401（2002）]，其中，对于矩形结构，作者获得了具有相同频率$k$但具有$κ\simδ$的同步模式。最后，我们发现，如果$w$是大相比，$a$，那么许多附近的模式有助于阻抗，导致在尾场，朗道阻尼。
英文摘要：
We consider the impedance of a structure with rectangular, periodic corrugations on two opposing sides of a rectangular beam tube. Using the method of field matching, we find the modes in such a structure. We then limit ourselves to the the case of small corrugations, but where the depth of corrugation is not small compared to the period. For such a structure we generate analytical approximate solutions for the wave number $k$, group velocity $v_g$, and loss factor $κ$ for the lowest (the dominant) mode which, when compared with the results of the complete numerical solution, agreed well. We find: if $w\sim a$, where $w$ is the beam pipe width and $a$ is the beam pipe half-height, then one mode dominates the impedance, with $k\sim1/\sqrt{wδ}$ ($δ$ is the depth of corrugation), $(1-v_g/c)\simδ$, and $κ\sim1/(aw)$, which (when replacing $w$ by $a$) is the same scaling as was found for small corrugations in a {\it round} beam pipe. Our results disagree in an important way with a recent paper of Mostacci {\it et al.} [A. Mostacci {\it et al.}, Phys. Rev. ST-AB, {\bf 5}, 044401 (2002)], where, for the rectangular structure, the authors obtained a synchronous mode with the same frequency $k$, but with $κ\simδ$. Finally, we find that if $w$ is large compared to $a$ then many nearby modes contribute to the impedance, resulting in a wakefield that Landau damps.
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